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An extension of data automata that captures XPath

Mikołaj Bojańczyk ; Sławomir Lasota.

We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automata-theoretic approach may be applied to answer decidability and expressibility questions for XPath.

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Two-Way Unary Temporal Logic over Trees

Mikolaj Bojanczyk.

We consider a temporal logic EF+F^-1 for unranked, unordered finite trees. The logic has two operators: EF\phi, which says "in some proper descendant \phi holds", and F^-1\phi, which says "in some proper ancestor \phi holds". We present an algorithm for deciding if a regular language of unranked&nbsp;[&hellip;]

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Wreath Products of Forest Algebras, with Applications to Tree Logics

Mikolaj Bojanczyk ; Igor Walukiewicz ; Howard Straubing.

We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and first-order logic over the ancestor relation. While the characterizations are in&nbsp;[&hellip;]

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Piecewise testable tree languages

Mikołaj Bojańczyk ; Luc Segoufin ; Howard Straubing.

This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma_1 sentences if and only if its&nbsp;[&hellip;]

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Boundedness in languages of infinite words

Mikołaj Bojańczyk ; Thomas Colcombet.

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions where two new variants of the Kleene star $L^*$ are&nbsp;[&hellip;]

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Undecidability of a weak version of MSO+U

Mikołaj Bojańczyk ; Laure Daviaud ; Bruno Guillon ; Vincent Penelle ; A. V. Sreejith.

We prove the undecidability of MSO on $\omega$-words extended with the second-order predicate $U_1(X)$ which says that the distance between consecutive positions in a set $X \subseteq \mathbb{N}$ is unbounded. This is achieved by showing that adding $U_1$ to MSO gives a logic with the same&nbsp;[&hellip;]

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